The first hitting time of the integers by symmetric Levy processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Isozaki, Yasuki¹ 

[1] Kyoto Inst Technol, Dept Arts & Sci, Sakyo Ku, Kyoto 6068585, Japan

关键词: Levy process;    Probabilistic potential theory;    Pick function;    Fractional linear transformations;   

DOI  :  10.1016/j.spa.2018.06.001

来源: Elsevier

【 摘 要 】

For one-dimensional Brownian motion, the exit time from an interval has finite exponential moments and its probability density is expanded in exponential terms. In this note we establish its counterpart for certain symmetric Levy processes. Applying the theory of Pick functions, we study properties of the Laplace transform of the first hitting time of the integer lattice as a meromorphic function in detail. Its density is expanded in exponential terms and the poles and the zeros of a Pick function play a crucial role. Intermediate results concerning finite exponential moments are also obtained for a class of nonsymmetric Levy processes. (C) 2018 Elsevier B.V. All rights reserved.

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